The centroid method of numerical integration

Summary The midpoint method of integration of a function of one variable is perhaps the simplest method of numerical integration, although it is often not mentioned in textbooks. It is here generalized to any number of dimensions and the generalization is called thecentroid method. This again is a very simple method and it can be conveniently used, for example, for the integration of a function of several variables over any non-pathological region. The numerical examples include the integration of multinormal integrands.     

Sparsity Inducing Prior Distributions for Correlation Matrices of Longitudinal Data

For longitudinal data, the modeling of a correlation matrix ?R can be a difficult statistical task due to both the positive definite and the unit diagonal constraints. Because the number of parameters increases quadratically in the dimension, it is often useful to consider a sparse parameterization. We introduce a pair of prior distributions on the set of correlation matrices for longitudinal data through the partial autocorrelations (PACs), which vary independently over (?1,1). The first prior shrinks each of the PACs toward zero with increasingly aggressive shrinkage in lag. The second prior (a selection prior) is a mixture of a zero point mass and a continuous component for each PAC, allowing for a sparse representation. The structure implied under our priors is readily interpretable for time-ordered responses because each zero PAC implies a conditional independence relationship in the distribution of the data. Selection priors on the PACs provide a computationally attractive alternative to selection on the elements of ?R or ?R^{? 1} for ordered data. These priors allow for data-dependent shrinkage/selection under an intuitive parameterization in an unconstrained setting. The proposed priors are compared to standard methods through a simulation study and illustrated using a multivariate probit data example. Supplemental materials for this article (appendix, data, and R code) are available online.     

Cell migration and polarity on microfabricated gradients of extracellular matrix proteins

This paper explores the effects of the surface density and concentration profiles of extra cellular matrix proteins on the migration of rat intestinal IEC-6 cells. Microfluidic devices were used to create linear, immobilized gradients of laminin. This study investigated both the impact of the steepness and local concentrations on the directedness of cell migration. The bulk concentrations of proteins in the feed streams in the mixing device determined the gradient profile and the local concentration of laminin in the device. Two sets of gradients were used to explore cell migration directedness: (i) gradients with similar change in local concentration, i.e., the same gradient steepness, and (ii) different gradients with similar local concentrations. Cells migrated up the gradients, independent of the steepness of the gradients used in this study. At the same local laminin concentration, the migration rate was independent of the gradient steepness. However, cell directedness decreased significantly at high laminin densities.     

Covariance Partition Priors: A Bayesian Approach to Simultaneous Covariance Estimation for Longitudinal Data

The estimation of the covariance matrix is a key concern in the analysis of longitudinal data. When data consist of multiple groups, it is often assumed the covariance matrices are either equal across groups or are completely distinct. We seek methodology to allow borrowing of strength across potentially similar groups to improve estimation. To that end, we introduce a covariance partition prior that proposes a partition of the groups at each measurement time. Groups in the same set of the partition share dependence parameters for the distribution of the current measurement given the preceding ones, and the sequence of partitions is modeled as a Markov chain to encourage similar structure at nearby measurement times. This approach additionally encourages a lower-dimensional structure of the covariance matrices by shrinking the parameters of the Cholesky decomposition toward zero. We demonstrate the performance of our model through two simulation studies and the analysis of data from a depression study. This article includes Supplementary Materials available online.     

A review of indirect searches for particle dark matter

The indirect detection of dark matter annihilation and decay using observations of photons, charged cosmic rays and neutrinos offers a promising means of identifying the particle nature of this elusive component of the universe. The last decade has seen substantial advances in observational data-sets, complemented by new insights from numerical simulations, which together have enabled for the first time strong constraints on dark matter particle models, and have revealed several intriguing hints of possible signals. This review provides an introduction to indirect detection methods and an overview of recent results in the field.     

Regiospecific control of protein expression in cells cultured on two-component counter gradients of extracellular matrix proteins

This work describes the use of microfluidic tools to generate covalently immobilized counter gradients of extracellular matrix (ECM) proteins laminin and collagen I. Using these platforms, we demonstrate control of the expression levels of two proteins linked to cell cycle progression by virtue of the spatial location of cells on the gradients, and hence by the local ECM environments in these devices. In contrast to physisorbed gradients, covalently immobilized protein patterns preserved the gradient fidelity, making long term cell studies feasible. This method of precisely controlling local cell environments is simple and broadly portable to other cell types and to other ECM proteins or soluble factors. Our approach promises to enable new investigations in cell biology that will contribute to the establishment of biological design rules for controlling cell growth, differentiation, and function.     

Efficient, thermally stable, second order nonlinear optical response in organic hybrid covalent/ionic self-assembled films

A covalent/electrostatic layer-by-layer self-assembly method was used to achieve polar ordering of a water soluble, reactive dye in the fabrication of nonlinear optical (NLO) films. We observed a quadratic relationship between the second harmonic intensity I2(omega) and bilayer number for all films made with Procion Brown MX-GRN, demonstrating that the polar ordering of the chromophores is consistent in each successive bilayer. As the ionic strength of the dye deposition solution was increased to 0.5 M NaCl, the of the films increased by approximately 250% to 50 x 10(-9) esu, with a corresponding average chromophore tilt angle of 38 degrees . This was attributed to increased shielding of the dye charges which led to higher chromophore density in the bilayers. The electrooptic coefficient for films of 50 bilayers fabricated at 0.5 M NaCl was 14 +/- 2 pm/V. Importantly, these films exhibited excellent thermal stability, with only a 10% decrease in (I2(omega))(1/2) after 36 h at 85 degrees C and then 24 h at 150 degrees C. Furthermore, the (I2(omega))(1/2) recovered completely upon cooling to room temperature. These results with a commodity textile dye point to the potential value of this class of reactive chromophores and this self-assembly method for fabrication of electrooptic materials at ambient conditions from aqueous solutions.     

Steady-state permeation of carbon dioxide through a miscible,glassy polymer blend

Steady-state permeation measurements are reported for carbon dioxide (CO₂) through quenched, amorphous films of a miscible blend of poly(butylene terephthalate) (PBT) and a random copolyester of bisphenol-A and iso/terephthalate acids (PAr). Permeabilities were determined at 35°C on blends with up to 60 wt % PBT and for CO₂ pressures up to 300 psi (2.06 MPa). At a fixed blend composition, the permeability, P̄, decays with driving pressure, p, as described by dual-mode models for gas transport in glassy polymers. From regression fits of the data to dual-mode model predictions for P̄(p), high-and low-pressure limiting permeabilities are determined. These decrease with PBT content in a manner indicating strong, favorable energetic interactions between the PBT and PAr components in the blend. © 1996 John Wiley & Sons, Inc.